Questions tagged [quantum-algorithms]
For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.
1,341 questions
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What is the biggest pain point for quantum developers? [closed]
I'm working on building an AI platform to streamline/automate the workflow for quantum developers. I was curious to learn from those who are actively involved in the field (building circuits, writing ...
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Quantum Phase Estimation
Implement the Quantum Phase Estimation (QPE) algorithm using the unitary operator S and the eigenstate
∣1⟩ as the target qubit. Use 3 counting qubits and 1 target qubit.
Assumptions / notation:
Assume ...
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Is this a correct DAG from parsing QASM?
Currently writing a QASM parser and wondering if this is the proper way to parse a program using a DAG (Deutsch's from QASMBench in this example).
The output from Deutsch's would be:
...
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A Symmetry in Shor’s Algorithm: Successful bases always come in pairs (a, N–a)
I’ve recently written a short note proving a structural property of Shor’s factoring algorithm, and I’d like feedback from those more experienced in quantum algorithms.
Key result:
If a base a is ...
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How to implement an exp{-iat}?
I'd like to implement $e^{-iat}$ as part of an algorithm for hamiltonian simulation. This makes the operation:
$$
|a\rangle|0\rangle \rightarrow |a\rangle e^{-iat}|0\rangle
$$
According to Nathan ...
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QSVT Phase Angles for Chebyshev Polynomials
I have a block-encoded matrix $A$ (for example, a diagonal matrix) encoded in a unitary $U_A$. I would like to apply a Chebyshev polynomial to the singular values of $A$ using Quantum Singular Value ...
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Best algorithm for reversible/quantum computation of the hamming weight of a bit-string
This question is similar to Hamming Weight algorithm , but the solutions to that question do not suffice to implement what i am looking for.
Does anybody know the best bound for a quantum circuit / ...
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Why QFT-based arithmetic?
In what follows, I am mostly interested in exact arbitrary-precision arithmetic. Quantum arithmetic is an active research topic. Of course any classical algorithm for arithmetic can be expressed as a ...
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Constant Quantum Modular Addition with input greater than modulus
I want to perform constant-quantum modular addition: $|x\rangle \mapsto |x + K \bmod R \rangle$ where the input $x$ can be greater than $R$. E.g. For $K=1, R=10$ the input $|11 \rangle$ should map to $...
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How can QPE be used to determine whether any eigenvalue of an arbitrary matrix is (close to) zero?
I'm trying to find whether there are any eigenvalue of an arbitrary matrix that is (close to) zero without measurement using quantum phase estimation (QPE). I am experimenting with the code below. I'm ...
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How to make a phase oracle that marks the largest number?
I have a list of strategies each with a corresponding score, I want my oracle to apply the phase shift on the strategy with the largest score value. Without knowing the values beforehand how would I ...
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Is there a way to assign different weights to and get the decoding edges from 2D graphs in each round when using pymatching to decode 3D graph
It seems that when decoding 3D graph, pymatching only gives the overall decoding edges and only takes spacelike-weights in 2D graph which means the weights are the same in each round.
So I'd like to ...
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Can We find a quantum algorithm that can output all the subgroups of a finite group?
Just a simple curiosity, can we find a quantum algorithm that can give us all the subgroups of a finite group?
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Understanding Quantum Singular Value Transformation from Gilyen et al, 2018
I try to understand the first pages of Gilyen et al, 2018 article introducing the Quantum Singular Value Transformation.
Here is a snapshot of the paragraph I have difficulties with :
This paragraph ...
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How to do phase kickback when both control and target qubits are in superposition and use sign of phase coherently to control further operations?
Using the following circuit, I’m trying to do phase kickback to qubit 3, $q_3$, to change its state to $|1\rangle$ when the phase of $|q_2,q_1,q_0\rangle=|111\rangle$ is negative and $|q_3\rangle=|0\...
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How to reset ancilla after swapping when original ancilla flipping condition is not available?
Following little-endian format, I have the following state, which is part of a larger superposition of 6 qubits:
$$
\alpha|0\rangle_{swap\_ancilla}|010010\rangle + \beta|0\rangle_{swap\_ancilla}|...
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What is exactly Observable learning task ? How does training work in observable learning for quantum machine learning?
I'm currently learning about observable learning in quantum machine learning. I understand that the goal is often to predict the expectation value of a given observable (like a Pauli operator or a ...
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Proof of Theorem 3 in Quantum Singular Value Transformation by Gilyen et al
I was recently going over the first proof in Gilyen et alia."Quantum singular value transformation and beyond:
exponential improvements for quantum matrix arithmetics" https://arxiv.org/abs/...
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How can we build a unitary that implements the negative identity operator
I just want to know how we can build a unitary (using arbitrary 1 or 2-local universal quantum gates) that implements the operator:
$- \mathbb{I}$.
So $\sum_x \alpha_x |x\rangle \mapsto \sum_x -\...
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How do I design a quantum circuit on $n$ qudits that implements a general unitary two-design?
How do I design a quantum circuit on $n$ qudits that implements a general unitary two-design either:
exactly (presumably using Clifford group), or
approximately 2-design
I am looking for a structure ...
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What are the ways in the current literature to simplify extremely large circuits?
Consider a 50-qubit circuits with 10s of thousands of gates, and with cz gates between every couple of qubits, how would this monster of a circuit be simplified to run on a quantum device?
Would we ...
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Failure case in Shor's algorithm
The answer to the following question https://math.stackexchange.com/questions/2856947/prove-lemma-order-of-x-mathrmmod-n-is-even-with-probability-1-2 shows that at least half of the elements in $\...
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Deprecation warnings for `Estimator` in new versions of Qiskit packages (`qiskit_aer >= 0.15`)
I have the following code which calculates and plots the ground state energy of a hydrogen molecule against the bond distance using Varitation Quantum Eigensolver (VQE) algorithm.
...
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Runtime Overhead of Quantum Error Correction in Large Quantum Algorithms
Has there been any research quantifying the runtime overhead incurred when implementing quantum error correction (QEC) compared to executing a quantum algorithm without QEC?
For instance,
With a ...
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Why Must We Remove Garbage for Interference Tests? Graph Isomorphism example
I am curious about quantum approaches to graph isomorphism and have encountered a recurring point: the necessity of cleaning up any garbage generated during state preparation. For example, take a look ...
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